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We prove the existence of a solution for an equation where the nonlinearity is singular at zero, namely - Δ u = (- u - β + f (u)) χ { u > 0 } in Ω ⊂ R 2 with Dirichlet boundary condition. The function f grows exponentially, which can be subcritical or critical with respect to the Trudinger–Moser embedding. We examine the functional I ϵ corresponding to the ϵ -perturbed equation - Δ u + g ϵ (u) = f (u) , where g ϵ tends pointwisely to u - β as ϵ → 0 + . We show that I ϵ possesses a critical point u ϵ in H 0 1 (Ω) , which converges to a genuine nontrivial nonnegative solution of the original problem as ϵ → 0 . We also address the problem with f(u) replaced by λ f (u) , when the parameter λ > 0 is sufficiently large. We give examples. [ABSTRACT FROM AUTHOR]

General expressions for statistical entropy analysis of vapor-compression refrigeration cycles are given. An open-source software for statistical entropy analysis of vapor-compression refrigeration cycles has been developed. Using the statistical entropy analysis method, two different refrigeration cycles that use an ejector as an expansion device were compared with 5 other cycles in which throttle valves are used as expansion devices. Calculations were made for two temperature levels: medium-temperature and low-temperature. Energy consumption levels are shown to depend on the cycle used and the boiling. The results showed the expedience and prospects of use of ejectors as expansion devices not only in transcritical, but also in subcritical refrigeration cycles. [ABSTRACT FROM AUTHOR]

We prove existence of two solutions for an elliptic equation with exponential growth on a bounded domain. The first solution is obtained by an approximation scheme together with a fixed point theorem. The second solution is found by variational methods, and its expression is given by the sum of the first solution by other adequate function. The nonlinearities may have subcritical, critical or supercritical exponential growth. [ABSTRACT FROM AUTHOR]

Rock environments both underground and on Earth's surface show indications of energetic macroscale fracture. In tunnels and excavations, these manifest as rockbursts—energetic explosions of rock that can damage engineering projects, and may pose ongoing financial and safety risk as rock stresses adjust during post-failure relaxation. In natural settings at the surface, evidence for rockbursts exist in the form of tent-like structures of ruptured exfoliation sheets, but few direct observations of such events exist, precluding the analysis of how natural rock formations may evolve after rupture. Here we investigate the post-failure evolution of a granitic rock dome following rapid fracture events (i.e., surficial rockbursts) that occurred in California, USA during 2014–2016. Building upon previous work that showed a thermal stress origin for the observed fracturing, we investigate the return to background stress conditions (i.e., stress relaxation) observed in both short- (week, month) and long-term (multi-year) rock deformation trends. Acoustic emissions, deformation, and environmental monitoring data indicate that partially detached rock sheets forming the surface of the dome undergo fracture aperture closing during cooling periods, concurrent with reduction of rock stress by the source of forcing (i.e., thermal stress). However, with sufficient critical and/or subcritical fracture, our observations also show that rock sheets can become decoupled from the source of stress, resulting in a long-term return to background stress conditions. Our results provide insight into the cyclic and likely ephemeral nature of rock fracture in surficial rock domes, as well as in underground rockburst environments. [ABSTRACT FROM AUTHOR]

As a central concept in fluid dynamics stability is fundamental in understanding transitions from laminar to turbulent flow. In continuum flows, it is well-established that a transition to turbulence can occur at subcritical Reynolds numbers, in contrast to theoretical predictions. In non-equilibrium molecular dynamics (NEMD), it has been widely observed that at a critical Reynolds number the fluid undergoes an ordering transition from an amorphous phase to a 'string' phase. Using the fluctuation theorem (FT) and the dissipation function, we generalize the classical continuum Reynolds-Orr equation to sheared molecular fluids by ascribing a natural description to the nature of stochastic perturbations, i.e. fluctuations in shear stress. Via the Poincaré inequality, we arrive at a new stability criterion by providing a lower bound on the exponential decay of perturbations, which reduces to the classical continuum result in the limit of infinite system size. We investigate the nature of these velocity perturbations and conditions necessary for growth in the kinetic energy of perturbations. We obtain a fluid dependent estimate for the critical Reynolds number by which one may estimate the critical Reynolds number at which the fluid transitions to the string phase, thus providing a framework for generalizing classical continuum theories to the microscale. [ABSTRACT FROM AUTHOR]

This paper visits the stability, bifurcations and post-critical behaviors of a nonlinear curved plate in a subsonic axial flow. The curved plate is simply supported and subjected to an initial horizontal tension. The plate is initially curved, and the initial shape is modeled by a shallow shell with constant curvature. The airflow is assumed incompressible, and the fluid force is considered as the sum of two parts: One is due to the plate deformation, and the other is to the plate initial shape. The Laplace's equation is solved for the fluid force by placing a series of time-independent sources on the plate. The nonlinear axial strain due to large deformation is considered for the potential energy of the plate. Results show that the system has a fundamental and four bifurcated equilibrium solutions. The fundamental bifurcation is always supercritical; however, the secondary bifurcation is either supercritical or subcritical. The bifurcation regions are analyzed in parametric planes, and eight typical bifurcation processes are explored. There appear jump phenomena between the two stable states of system after the fundamental bifurcation. The combinations of designed parameters, including the plate initial curvature, horizontal tension and flow velocity, highly influence the bifurcation behaviors of the plate. [ABSTRACT FROM AUTHOR]

In this study, the effects of environment conditions on decane were investigated. Decane was injected in subcritical and supercritical ambient conditions. The visualization chamber was pressurized to 1.68 MPa by using nitrogen gas at a temperature of 653 K for subcritical ambient conditions. For supercritical ambient conditions, the visualization chamber was pressurized to 2.52 MPa by using helium at a temperature of 653 K. The decane injection in the pressurized chamber was visualized via a shadowgraph technique and gradient images were obtained by a post processing method. A large variation in density gradient was observed at jet interface in the case of subcritical injection in subcritical ambient conditions. Conversely, for supercritical injection in supercritical ambient conditions, a small density gradient was observed at the jet interface. In a manner similar to that observed in other cases, supercritical injection in subcritical ambient conditions differed from supercritical ambient conditions such as sphere shape liquid. Additionally, there were changes in the interface, and the supercritical injection core width was thicker than that in the subcritical injection. Furthermore, in cases with the same injection conditions, the change in the supercritical ambient normalized core width was smaller than the change in the subcritical ambient normalized core width owing to high specific heat at the supercritical injection and small phase change at the interface. Therefore, the interface was affected by the changing ambient condition. Given that the effect of changing the thermodynamic properties of propellants could be essential for a variable thrust rocket engine, the effects of the ambient conditions were investigated experimentally. [ABSTRACT FROM AUTHOR]

In this work, we introduce and study the well-posedness of the multidimensional fractional stochastic Navier-Stokes equations on bounded domains and on the torus (briefly dD-FSNSE). For the subcritical regime, we establish thresholds for which a maximal local mild solution exists and satisfies required space and time regularities. We prove that under conditions of Beale-Kato-Majda type, these solutions are global and unique. These conditions are automatically satisfied for the 2D-FSNSE on the torus if the initial data has H-regularity and the diffusion term satisfies growth and Lipschitz conditions corresponding to H-spaces. The case of 2D-FSNSE on the torus is studied separately. In particular, we established thresholds for the global existence, uniqueness, space and time regularities of the weak (strong in probability) solutions in the subcritical regime. For the general regime, we prove the existence of a martingale solution and we establish the uniqueness under a condition of Serrin's type on the fractional Sobolev spaces. [ABSTRACT FROM AUTHOR]

In this paper, the current status of amino acid extraction from animal waste biomass and reducing sugar from plant waste biomass by hydrolysis in subcritical and supercritical water was reviewed. The properties of subcritical and supercritical water, reactor systems, reaction kinetics, reaction mechanism, and effects of different factors (temperature, time, and catalyst) on yield were summarized. Subcritical and supercritical water hydrolysis is a biorefinery approach for both protein and sugar-one treatment. Hydrolysis at subcritical and supercritical conditions may provide an efficient process for recovering useful chemicals from biomass wastes and for the disposal of biomass wastes. [ABSTRACT FROM AUTHOR]

We investigate the effectiveness of linear and nonlinear time-delay feedback controls to suppress high amplitude oscillations of an elastically mounted square cylinder undergoing galloping oscillations. A representative model that couples the transverse displacement and the aerodynamic force is used. The quasi-steady approximation is used to model the galloping force. A linear analysis is performed to investigate the effect of linear time-delay controls on the onset speed of galloping and natural frequencies. It is demonstrated that a linear time-delay control can be used to delay the onset speed of galloping. The normal form of the Hopf bifurcation is then derived to characterize the type of the instability (supercritical or subcritical) and to determine the effects of the linear and nonlinear time-delay parameters on their outputs near the bifurcation. The results show that the nonlinear time-delay control can be efficiently implemented to significantly reduce the galloping amplitude and suppress any dangerous behavior by converting any subcritical Hopf bifurcation into a supercritical one. [ABSTRACT FROM AUTHOR]

An investigation on subcritical spheroidization anneal of the cold-rolled 50CrV4 steel at 720 °C has been carried out. During spheroidization anneal, the lamellar cementite was gradually broken down and changed to spherical shape. With prolonging of soaking time, the amount of lamellar cementite decreases gradually, and that of the spheroidized cementite particle increases gradually. The relationship of the spheroidization ratio versus soaking time for the steel can be described by a typically sigmoid curve. Additionally, the cold rolling deformation accelerates the breakup of lamellar cementite and the formation of spheroidal cementite particles during spheroidization anneal of the steel. The more severe the deformation is, the more rapidly the spheroidization occurs. From the results of tensile and hardness test, the yield strength, ultimate tensile strength, and hardness decrease and the percentage elongation to failure increases rapidly during the first 2 h of spheroidization. Between 2 and 8 h, the yield strength, ultimate tensile strength, hardness nearly keep a constant, which are independent of the soaking time, whereas the percentage elongation to failure firstly increases and then decreases with prolonging of soaking time. [ABSTRACT FROM AUTHOR]

Poly( l-lactide) (PLLA) nanoparticles loaded with asiatic acid (AA) were successfully produced by rapid expansion of a subcritical solution into an aqueous receiving solution containing a dispersing agent. A mixture of carbon dioxide (CO) and ethanol (EtOH) with a weight ratio of 1:1 was used as the solvent for AA and PLLA. Two surfactants, Pluronic F127 and sodium dodecyl sulfate were employed. The former was found to be more effective for stabilizing AA-loaded PLLA nanoparticles, as a rapid expansion into a 0.1 wt% Pluronic F127 solution produced a stable nanosuspension consisting mainly of well-dispersed, individual nanoparticles. The effects of rapid expansion-processing conditions-AA to PLLA weight ratio and pre-expansion temperature (T)-on the size and morphology of composite nanoparticles, and the loading capacity and entrapment efficiency of AA in PLLA nanoparticles, were systematically investigated. It was found that AA-loaded PLLA nanoparticles with a size range of 30-100 nm were consistently fabricated by rapid expansion at T of 70-100 °C and AA to PLLA weight ratios of 1:2 and 1:4, and with a constant pre-expansion pressure of 330 bar. The T and AA to PLLA weight ratio had no significant effects on the size of the nanoparticles. The AA to PLLA weight ratio is a controlling parameter for both the loading capacity and the entrapment efficiency of AA in PLLA nanoparticles. The loading capacity and entrapment efficiency increased from 8-11 to 16-21 wt%, and 38-57 to 50-62 wt%, respectively, when the AA to PLLA weight ratio changed from 1:4 to 1:2. However, increasing the T from 70 to 100 °C decreased both the loading capacity and entrapment efficiency of AA in PLLA nanoparticles by ~20-30%. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study some inferential problems arising from the class of bisexual Galton-Watson branching processes with immigration of females and males (BGWPI). Immigrants are assumed to be unobservable, and it is only possible to sample the number of females, males, and couples (mating units) in each generation. Under these conditions, weighted conditional least square estimators are proposed for the offspring and immigration mean vectors. Asymptotic properties of such estimators are investigated when the process is subcritical and supercritical, paying especial attention to their strong consistency and limit distributions. Weighted conditional least square estimators are also developed for the offspring and immigration variance vectors, and their asymptotic properties are studied. Some comments on the critical case are also given to possibly provide a unified estimation theory for BGWPI. [ABSTRACT FROM AUTHOR]

We analyze the exponential decay property of solutions of the semilinear wave equation in bounded domain Ω of R N with a damping term which is effective on the exterior of a ball and boundary conditions of the Cauchy-Ventcel type. Under suitable and natural assumptions on the nonlinearity, we prove that the exponential decay holds locally uniformly for finite energy solutions provided the nonlinearity is subcritical at infinity. Subcriticality means, roughly speaking, that the nonlinearity grows at infinity at most as a power p < 5. The results obtained in R 3 and R N by B. Dehman, G. Lebeau and E. Zuazua on the inequalities of the classical energy (which estimate the total energy of solutions in terms of the energy localized in the exterior of a ball) and on Strichartz’s estimates, allow us to give an application to the stabilization controllability of the semilinear wave equation in a bounded domain of R N with a subcritical nonlinearity on the domain and its boundary, and conditions on the boundary of Cauchy-Ventcel type. [ABSTRACT FROM AUTHOR]

The Hopf bifurcations of an airfoil flutter system with a cubic nonlinearity are investigated, with the flow speed as the bifurcation parameter. The center manifold theory and complex normal form method are used to obtain the bifurcation equation. Interestingly, for a certain linear pitching stiffness the Hopf bifurcation is both supercritical and subcritical. It is found, mathematically, this is caused by the fact that one coefficient in the bifurcation equation does not contain the first power of the bifurcation parameter. The solutions of the bifurcation equation are validated by the equivalent linearization method and incremental harmonic balance method. [ABSTRACT FROM AUTHOR]

Steady-state MHD flows in channels of the nozzle type in the presence of an external longitudinal magnetic field can be divided into two significantly different classes. Subcritical flows, in which the Alfvén velocity calculated from the longitudinal magnetic field is less than the plasma velocity, have mainly the same properties as flows in a transverse magnetic self-field and their quantitative characteristics depend only slightly on the longitudinal magnetic field strength. Supercritical flows with the opposite inequality for the velocities correspond to strong longitudinal magnetic field. The main difference is the transitions between different forms of energy (kinetic, thermal, and electromagnetic). The present study contains a classification of possible flows, namely, sub- and supercritical and sub-, super-, and transonic flows with respect to the fast and slow magnetosonic and Alfvén velocities. Examples of these flows are given. The effect of the problem parameters on the flow properties is investigated. [ABSTRACT FROM AUTHOR]

SCWO, sometimes referred to as hydrothermal waste processing, uses the solvating traits of water in its supercritical condition to effectively destroy liquid organic wastes. One major problem in the supercritical water oxidation process is corrosion, because all metallic tubes in the process are exposed to high temperature and high pressure as well as severe corrosive species such as Cl−, F−, S2−, and O2−. The presence of Cl− when the pH of a solution is very low and the solution has excess oxygen causes active corrosion and metal loss by metal-chloride and/or oxychloride formation. This study performed a chromizing treatment on 316 stainless steel and immersion tests in supercritical water. Weight change of chromized steels and untreated steels was measured, and the chemical state and composition of oxide films on 316 stainless steel were investigated. On the basis of SCWO tests using distilled water, the oxide layer was found to be very thin and homogeneous and weight gain was observed regardless of testing temperature, while the chromizing treatment slightly reduced weight gain. In the case of SCWO tests using salt water, weight loss was observed regardless of testing temperature and its corrosion mode was pitting by chloride ion, while chromizing treatment greatly decreased the corrosion rate. [ABSTRACT FROM AUTHOR]

Starting from nonlinear equations on the f-plane containing frictional dissipation under the Boussinesq approximation, a new kind of generalized energy is proposed as the Lyapunov function, and averages are taken as any functions of ( x, z) instead of the commonly-used means of bilinear functions of ( x, z), thereby resulting in a new criterion of generalized nonlinear symmetric stability. It shows that not only must the dissipative coefficient be greater than a certain critical value but the initial disturbance amplitude must be synchronously smaller than another marginal value as well. It follows that the latter imposes a crucial constraint on the former, thus leading to the fact that when the amplitude is bigger compared to another critical value, generalized nonlinear subcritical symmetrical instability may occur. The new criterion contributes greatly to the improvement of the previous results of its kind. [ABSTRACT FROM AUTHOR]

The objectives of this investigation are to show the feasibility of producing large monoliths with minimal shrinkage at subcritical conditions, and to understand the drying behavior. Crack-free SiO2 monoliths (5.6 cm in diameter and 25 cm in length) were repeatedly dried with little shrinkage (<2%). Some gels showed increasing shrinkage with decreasing pressure. However, this shrinkage was reduced to negligible levels at conditions considerably less than supercritical pressure by increasing both the pore size and the gel strength. This moderate pressure drying (MPD) process may make aerogel fabrication economically more feasible due to reduced pressure chamber costs. [ABSTRACT FROM AUTHOR]

Three destructive mining shocks successively occurred nearby the seismic Station No.6 located in a shaft of the Fangshan Coal Mine of Beijing Mining Service in 4 minutes at 19 o’clock of May 15, 1993. The largest shock is of M=2.3 ( M 0=1.5×1011 N·m). Analysis of synthetic seismogram provides that the three shocks exhibited predominantly a dip-slip movement mode, which is consistent with the collapse of coal mass from the coal bed at high dip-angle, as observed by those who were present at the site. The near-field records of the main shock and a series of events prior to it made at the Station No.6 are different from normal records, it had not only high-frequency vibration, but also low-frequency vibration. By using elastic wave theory and nucleation theory of seismic fracture during recent years, analysis of the data indicates that the low-frequency vibration maybe long-period wave as the subcritical extension is pushing forward. It is an unrecovered deformation. The high-frequency vibration is just the mining shock event, exhibiting a wave field of brittle fracture radiation. From the dominant frequency of low-frequency vibration in the records of M=2.3 event and the records of foreshocks at 5.4 s before it, it is inferred that the volume of dilatation zone at the termination of shock-generating fracture has rapidly enlarged during the occurrence of the main shock. In 20 or more days before the main shock, the source process was of the following characteristics: the subcritical extension occurred for many times; during this period the volume of dilatation zone at the termination of shock-generating fracture little changed. The subcritical extension not only exits long-period waves, but also induced small events at the same time. The dominant orientation of subcritical extension is basically consistent with the direction of slip movement during main shock. [ABSTRACT FROM AUTHOR]

We introduce and study the well posedness: global existence, uniqueness and regularity of the solutions, of a class of d-dimensional fractional stochastic active scalar equations defined either on the torus T d or R d or O ⊊ R d bounded, d ≥ 1 . This class includes, among others the stochastic; dD-quasi-geostrophic equation, fractional Burgers equation, fractional nonlocal transport equation and the 2D-fractional vorticity Navier–Stokes equation. We consider a locally Lipschitz diffusion term and a cylindrical Q-Wiener process with finite trace covariance Q. In particular, for O = T d or O ⊊ R d bounded, we prove the existence and the uniqueness of a global mild solution for the free divergence mode in the subcritical regime ( α > α 0 (d) ≥ 1 ), martingale solutions in the general regime ( α ∈ (0 , 2) , supercritical, critical and subcritical) and free divergence mode and a local mild solution for the general mode and subcritical regime. Different kinds of regularity are also established for these solutions. For O = R d , we studied the subcritical regime and we proved the existence of a global martingale solution for the free divergence mode and a local mild solution for the general mode. [ABSTRACT FROM AUTHOR]